Movies and Sleep Habits Adapted From: “Choosing Random Samples” in Samples and Populations activities from Connected Mathematics 2 Reference: Lappan, G. Michigan State University. National Science Foundation (U.S.). Pearson Education, I., & Connected Mathematics (Project). (2009). Connected mathematics. 2[nd ed.] Boston, Mass.: Pearson.
CCSS-M Content Standards: 6.SP (1-5), 7.SP.1 and 7.SP.2 and leads into 7.SP.3 and 7.SP.4 CCSS-M Practices: 1, 2, 3, 5, and 8
Task: *Note: This task requires some familiarity with TinkerPlots. Also, students will work in groups for this activity.
Teacher launches the activity by asking students, “How many movies did you watch last week? How many hours of sleep did you get on average last week?”
Teacher passes out the student handout for the activity and introduces it as an investigation of students’ sleep habits and movie-watching frequency. Note: Data files can be found here.
Allow students time to read the activity along with the teacher and discuss how they would classify “movies.” For example, students may consider only movies they watched in the theater or those they also watched at home by renting or watching them on television. Teacher discusses the importance of deciding on this interpretation when analyzing data.
Through this discussion, teacher asks the class to come to a consensus on the interpretation of the number of movies reported on the survey so that all conclusions and interpretations of results are considered using the same view of the data.
Students begin working on the activity. Once data has been collected, students enter their data into TinkerPlots and explore the questions posed on the handout. Each student works on their own computer but observes their groups’ results as well. The goal is for students to make informal inferences about the data they’ve investigated.
Once students have completed their activity, teacher brings the class back together to discuss each group’s findings.
PD Agenda: Length of session:2 hours Materials needed:Computer with Tinkerplots software installed; Random number generator (or spinner) *Note: Facilitators will model how the lesson should be carried out in the classroom with pedagogical discussions interwoven throughout. All time lengths listed below following each component of the activity are estimates and not strict time allotments.
Participants (teachers) are seated in groups of 2-3 to encourage discussion and collaboration.
Facilitators conduct a brief tutorial on Tinkerplots with participants to help them become familiar with the graphical representations of data available on the software. This will be done with an abstract set of data (out of context, so that the focus is on learning the technology). (25 minutes)
Once participants feel comfortable with the software, the facilitators conduct the class activity as the teachers would with their students. Facilitators launch the activity by asking the participants, “How many movies did you watch last week? How many hours of sleep did you get on average last week?” (5 minutes)
Facilitators pass out the student handout (linked here Student Handout linked) for the activity and conducts a group discussion about how to classify “movies”.
Some questions to be considered may include:
Do “movies watched” include only those seen in the theater?
Do we include movies watched on DVD’s at home?
Do we include movies downloaded on the internet?
Do we only count movies that are seen in their entirety?
The entire group ultimately decides on the interpretation of the data provided in the table. Facilitators discuss the importance of deciding on this interpretation when analyzing data. (10 minutes)
Participants begin working on the activity in their groups. Once data has been collected, they enter their data into TinkerPlots and explore the questions posed on the handout. Each participant works on their own computer but observes their groups’ results as well. The goal is for them to make informal inferences about the data they’ve investigated. (30 minutes)
As participants are working, the facilitators circulate to monitor and select participant strategies to highlight in the whole group discussion that will follow. The facilitators will also decide on an appropriate sequence for group presentations that will promote the goal of the lesson. For example, the facilitators might select a group that chose to use a boxplot to display the sleep habits data and then another group that chose a dotplot. They may then select a group that used bins to organize their analysis and another group that used measures of center to help describe their data. The sequence will vary based on the approaches created by the participants.
As participants present, allow time for questions from other participants and facilitators for any needed clarifications. Facilitators should ensure the pair fully communicates their approach and justifies their inference. If evidence is not presented nor questioned by others, the facilitators should guide the presenters to provide their justification. (30 minutes)
After presentations, facilitators hold a discussion about the task. (20 minutes)
Questions might include:
What did you like about the task? Not like?
What was challenging?
What did you think about the other approaches presented?
Would you modify this task for your classroom? If so, how? If not, why?
What do you anticipate your students to like about this task? Dislike?
Is the task engaging enough for students? Explain.
What are some problems that may arise during the implementation of this task?
What are some misconceptions students might have during this task?
What could you do to alleviate some of these problems/misconceptions without taking away from the discovery?
Why the task would promote conceptual understanding of this topic and if it lays the foundation for other topics in statistics: With this task, students learn the importance of sampling randomly and the affect sampling with bias can have on the inferences they can make based on their data. In addition, as students work in groups collecting a number of samples from the same population, they have the opportunity to analyze repeated samples and investigate questions of variability among those samples. Through their explorations of their samples using technology, students also have the opportunity to pose and address questions related to measures of center, distribution and spread as they work to draw conclusions about sleep habits and movie-watching habits among people their age as well as a relationship between those variables. This lays a foundation for further study of those descriptive measures of data and how those measures help us analyze data. In addition, the final exploration of the relationship between the variables presents students with an introduction to bivariate data analysis. A focus on drawing conclusions in context is reinforced as students use technology that allows them to explicitly view the attributes relevant to their exploration (e.g. sleep habits on the x-axis and number of movies watched on the y-axis).
Movies and Sleep Habits
Adapted From: “Choosing Random Samples” in Samples and Populations activities from Connected Mathematics 2
Reference: Lappan, G. Michigan State University. National Science Foundation (U.S.). Pearson Education, I., & Connected Mathematics (Project). (2009). Connected mathematics. 2[nd ed.] Boston, Mass.: Pearson.
CCSS-M Content Standards: 6.SP (1-5), 7.SP.1 and 7.SP.2 and leads into 7.SP.3 and 7.SP.4
CCSS-M Practices: 1, 2, 3, 5, and 8
Task:
*Note: This task requires some familiarity with TinkerPlots. Also, students will work in groups for this activity.
- Teacher launches the activity by asking students, “How many movies did you watch last week? How many hours of sleep did you get on average last week?”
- Teacher passes out the student handout for the activity and introduces it as an investigation of students’ sleep habits and movie-watching frequency. Note: Data files can be found here.
- Allow students time to read the activity along with the teacher and discuss how they would classify “movies.” For example, students may consider only movies they watched in the theater or those they also watched at home by renting or watching them on television. Teacher discusses the importance of deciding on this interpretation when analyzing data.
- Through this discussion, teacher asks the class to come to a consensus on the interpretation of the number of movies reported on the survey so that all conclusions and interpretations of results are considered using the same view of the data.
- Students begin working on the activity. Once data has been collected, students enter their data into TinkerPlots and explore the questions posed on the handout. Each student works on their own computer but observes their groups’ results as well. The goal is for students to make informal inferences about the data they’ve investigated.
- Once students have completed their activity, teacher brings the class back together to discuss each group’s findings.
PD Agenda:Length of session: 2 hours
Materials needed: Computer with Tinkerplots software installed; Random number generator (or spinner)
*Note: Facilitators will model how the lesson should be carried out in the classroom with pedagogical discussions interwoven throughout. All time lengths listed below following each component of the activity are estimates and not strict time allotments.
- Participants (teachers) are seated in groups of 2-3 to encourage discussion and collaboration.
- Facilitators conduct a brief tutorial on Tinkerplots with participants to help them become familiar with the graphical representations of data available on the software. This will be done with an abstract set of data (out of context, so that the focus is on learning the technology). (25 minutes)
- Once participants feel comfortable with the software, the facilitators conduct the class activity as the teachers would with their students. Facilitators launch the activity by asking the participants, “How many movies did you watch last week? How many hours of sleep did you get on average last week?” (5 minutes)
- Facilitators pass out the student handout (linked here Student Handout linked) for the activity and conducts a group discussion about how to classify “movies”.
- Do “movies watched” include only those seen in the theater?
- Do we include movies watched on DVD’s at home?
- Do we include movies downloaded on the internet?
- Do we only count movies that are seen in their entirety?
- The entire group ultimately decides on the interpretation of the data provided in the table. Facilitators discuss the importance of deciding on this interpretation when analyzing data. (10 minutes)
- Participants begin working on the activity in their groups. Once data has been collected, they enter their data into TinkerPlots and explore the questions posed on the handout. Each participant works on their own computer but observes their groups’ results as well. The goal is for them to make informal inferences about the data they’ve investigated. (30 minutes)
- As participants are working, the facilitators circulate to monitor and select participant strategies to highlight in the whole group discussion that will follow. The facilitators will also decide on an appropriate sequence for group presentations that will promote the goal of the lesson. For example, the facilitators might select a group that chose to use a boxplot to display the sleep habits data and then another group that chose a dotplot. They may then select a group that used bins to organize their analysis and another group that used measures of center to help describe their data. The sequence will vary based on the approaches created by the participants.
- As participants present, allow time for questions from other participants and facilitators for any needed clarifications. Facilitators should ensure the pair fully communicates their approach and justifies their inference. If evidence is not presented nor questioned by others, the facilitators should guide the presenters to provide their justification. (30 minutes)
- After presentations, facilitators hold a discussion about the task. (20 minutes)
- What did you like about the task? Not like?
- What was challenging?
- What did you think about the other approaches presented?
- Would you modify this task for your classroom? If so, how? If not, why?
- What do you anticipate your students to like about this task? Dislike?
- Is the task engaging enough for students? Explain.
- What are some problems that may arise during the implementation of this task?
- What are some misconceptions students might have during this task?
- What could you do to alleviate some of these problems/misconceptions without taking away from the discovery?
Why the task would promote conceptual understanding of this topic and if it lays the foundation for other topics in statistics:Some questions to be considered may include:
Questions might include:
With this task, students learn the importance of sampling randomly and the affect sampling with bias can have on the inferences they can make based on their data. In addition, as students work in groups collecting a number of samples from the same population, they have the opportunity to analyze repeated samples and investigate questions of variability among those samples. Through their explorations of their samples using technology, students also have the opportunity to pose and address questions related to measures of center, distribution and spread as they work to draw conclusions about sleep habits and movie-watching habits among people their age as well as a relationship between those variables. This lays a foundation for further study of those descriptive measures of data and how those measures help us analyze data. In addition, the final exploration of the relationship between the variables presents students with an introduction to bivariate data analysis. A focus on drawing conclusions in context is reinforced as students use technology that allows them to explicitly view the attributes relevant to their exploration (e.g. sleep habits on the x-axis and number of movies watched on the y-axis).
Data Files